Average Error: 58.2 → 0.0
Time: 24.2s
Precision: 64
\[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
↓
\[\tanh x\]
\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}
↓
\tanh x
double f(double x) {
        double r3465727 = x;
        double r3465728 = exp(r3465727);
        double r3465729 = -r3465727;
        double r3465730 = exp(r3465729);
        double r3465731 = r3465728 - r3465730;
        double r3465732 = r3465728 + r3465730;
        double r3465733 = r3465731 / r3465732;
        return r3465733;
}
↓
double f(double x) {
        double r3465734 = x;
        double r3465735 = tanh(r3465734);
        return r3465735;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.2

    \[\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied tanh-undef0.0

    \[\leadsto \color{blue}{\tanh x}\]

  4. Final simplification0.0

    \[\leadsto \tanh x\]

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic tangent"
  (/ (- (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))